$\backslash$begin$\{$tabular$\}\{|$lcrr$|\}$

$\backslash$hline Constraint & Television & Radio & Online $\backslash \backslash$

$\backslash$hline Audience per advertisement & $110,000$ & $17,000$ & $30,000\backslash \backslash$

Cost per advertisement & $\backslash (\backslash$$ $2,500\backslash )$ & $\backslash (\backslash$$ $300\backslash )$ & $\backslash (\backslash$$ $500\backslash )\backslash \backslash$

Maximum media usage & $10$ & $23$ & $10\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$($a$)$ If the promotional budget is limited to $\backslash (\backslash$$ $20,500\backslash ),$ how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter $"0".$

$\backslash$begin$\{$tabular$\}\{|$lr$|\}$

$\backslash$hline Advertisement Alternatives & $\backslash$begin$\{$tabular$\}\{$c$\}$

No of commercial $\backslash \backslash$

messages

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline Television $\backslash \backslash$

Radio $\backslash \backslash$

Online $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

What is the allocation of the budget among the three media?

$\backslash$begin$\{$tabular$\}\{|$lc$|\}$

$\backslash$hline Advertisement Alternatives & Budget Allocation $\backslash \backslash$

$\backslash$hline Television & $\backslash (\backslash$vdots $\backslash )\backslash \backslash$

Radio & $\backslash (\backslash$$ $\backslash )\backslash \backslash$

Online & $\backslash (\backslash$square $\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

What is the total audience reached?

$($b$)$ By how much would audience contact increase if an extra $\backslash (\backslash$$ $100\backslash )$ were allocated to the promotional budget? Round your answer to the nearest whole number. Increase in audience coverage of approximately